1,093 research outputs found
Diffraction catastrophes and semiclassical quantum mechanics for Veselago lensing in graphene
We study the effect of trigonal warping on the focussing of electrons by n-p
junctions in graphene. We find that perfect focussing, which was predicted for
massless Dirac fermions, is only preserved for one specific sample orientation.
In the general case, trigonal warping leads to the formation of cusp caustics,
with a different position of the focus for graphene's two valleys. We develop a
semiclassical theory to compute these positions and find very good agreement
with tight-binding simulations. Considering the transmission as a function of
potential strength, we find that trigonal warping splits the single Dirac peak
into two distinct peaks, leading to valley polarization. We obtain the
transmission curves from tight-binding simulations and find that they are in
very good agreement with the results of a billiard model that incorporates
trigonal warping. Furthermore, the positions of the transmission maxima and the
scaling of the peak width are accurately predicted by our semiclassical theory.
Our semiclassical analysis can easily be carried over to other Dirac materials,
which generally have different Fermi surface distortions.Comment: 6 pages, 4 figures, plus supplemental material. Important reference
added and text update
Economic Growth and Longevity Risk with Adverse Selection
We study a closed economy featuring heterogeneous agents and exhibiting endogenous economic growth due to interfirm external effects. Individual agents differ in terms of their mortality profile. At birth, nature assigns a health status to each agent. Health type is private information and annuity firms can only observe an agent’s age. In the presence of longevity risk, agents want to annuitize their wealth conform the classic result by Yaari (1965). In the first-best case with perfect annuities, the market would feature a separating equilibrium (SE) in which each health type obtains an actuarially fair perfect insurance. In the SE all agents are savers throughout their lives. The informational asymmetry precludes the attainment of the first-best equilibrium, however, as healthy individuals have a strong incentive to misrepresent their type by claiming to be unhealthy. Using the equilibrium concept of Pauly (1974) and Abel (1986), we prove the existence of a second-best pooling equilibrium (PE) in which individuals of all types annuitize at a common pooling rate. As the unhealthy get close to their maximum attainable age, the pooling rate prompts such individuals to become net borrowers. But borrowing would reveal their health status, so the best the unhealthy can do is to impose a borrowing constraint on themselves during their autumn years. Using a plausibly calibrated version of the model we find that the growth- and welfare effects of PE versus SE are rather small, whilst those of PE versus no annuities at all (NAE) are rather large. An imperfect insurance is better than no insurance at all, both at the microeconomic and at the macroeconomic level.annuity markets, adverse selection, endogenous growth, overlapping generations, demography
The Tragedy of Annuitization
We construct a tractable discrete-time overlapping generations model of a closed economy and use it to study government redistribution of accidental bequests and private annuities in general equilibrium. Individuals face longevity risk as there is a positive probability of passing away before the retirement period. We find non-pathological cases where it is better for longrun welfare to waste accidental bequests than to give them to the elderly. Next we study the introduction of a perfectly competitive life insurance market offering actuarially fair annuities. There exists a tragedy of annuitization: although full annuitization of assets is privately optimal it is not socially beneficial due to adverse general equilibrium repercussions.Longevity risk, Risk sharing, Overlapping generations, Intergenerational transfers, Annuity markets
The Tragedy of Annuitization
We construct a tractable discrete-time overlapping generations model of a closed economy and use it to study government redistribution of accidental bequests and private annuities in general equilibrium. Individuals face longevity risk as there is a positive probability of passing away before the retirement period. We find non-pathological cases where it is better for long-run welfare to waste accidental bequests than to give them to the elderly. Next we study the introduction of a perfectly competitive life insurance market offering actuarially fair annuities. There exists a tragedy of annuitization: although full annuitization of assets is privately optimal it is not socially beneficial due to adverse general equilibrium repercussions.longevity risk, risk sharing, overlapping generations, intergenerational transfers, annuity markets
Harbour porpoises (Phocoena phocoena) and wind farms: a case study in the Dutch North Sea
The rapid increase in development of offshore wind energy in European waters has raised concern for the possible environmental impacts of wind farms. We studied whether harbour porpoise occurrence has been affected by the presence of the Dutch offshore wind farm Egmond aan Zee. This was done by studying acoustic activity of porpoises in the wind farm and in two reference areas using stationary acoustic monitoring (with T-PODs) prior to construction (baseline: June 2003 to June 2004) and during normal operation of the wind farm (operation: April 2007 to April 2009). The results show a strong seasonal pattern, with more activity recorded during winter months. There was also an overall increase in acoustic activity from baseline to operation, in line with a general increase in porpoise abundance in Dutch waters over the last decade. The acoustic activity was significantly higher inside the wind farm than in the reference areas, indicating that the occurrence of porpoises in this area increased as well. The reasons of this apparent preference for the wind farm area are not clear. Two possible causes are discussed: an increased food availability inside the wind farm (reef effect) and/or the absence of vessels in an otherwise heavily trafficked part of the North Sea (sheltering effect
Modeling Klein tunneling and caustics of electron waves in graphene
We employ the tight-binding propagation method to study Klein tunneling and
quantum interference in large graphene systems. With this efficient numerical
scheme, we model the propagation of a wave packet through a potential barrier
and determine the tunneling probability for different incidence angles. We
consider both sharp and smooth potential barriers in n-p-n and n-n' junctions
and find good agreement with analytical and semiclassical predictions. When we
go outside the Dirac regime, we observe that sharp n-p junctions no longer show
Klein tunneling because of intervalley scattering. However, this effect can be
suppressed by considering a smooth potential. Klein tunneling holds for
potentials changing on the scale much larger than the interatomic distance.
When the energies of both the electrons and holes are above the Van Hove
singularity, we observe total reflection for both sharp and smooth potential
barriers. Furthermore, we consider caustic formation by a two-dimensional
Gaussian potential. For sufficiently broad potentials we find a good agreement
between the simulated wave density and the classical electron trajectories.Comment: 14 pages, 12 figure
Electronic optics in graphene in the semiclassical approximation
We study above-barrier scattering of Dirac electrons by a smooth
electrostatic potential combined with a coordinate-dependent mass in graphene.
We assume that the potential and mass are sufficiently smooth, so that we can
define a small dimensionless semiclassical parameter . This electronic
optics setup naturally leads to focusing and the formation of caustics, which
are singularities in the density of trajectories. We construct a semiclassical
approximation for the wavefunction in all points, placing particular emphasis
on the region near the caustic, where the maximum of the intensity lies.
Because of the matrix character of the Dirac equation, this wavefunction
contains a nontrivial semiclassical phase, which is absent for a scalar wave
equation and which influences the focusing. We carefully discuss the three
steps in our semiclassical approach: the adiabatic reduction of the matrix
equation to an effective scalar equation, the construction of the wavefunction
using the Maslov canonical operator and the application of the uniform
approximation to the integral expression for the wavefunction in the vicinity
of a caustic. We consider several numerical examples and show that our
semiclassical results are in very good agreement with the results of
tight-binding calculations. In particular, we show that the semiclassical phase
can have a pronounced effect on the position of the focus and its intensity.Comment: 103 pages, 11 figure
Mapping individual electromagnetic field components inside a photonic crystal
We present a method to map the absolute electromagnetic field strength inside
photonic crystals. We apply the method to map the electric field component Ez
of a two-dimensional photonic crystal slab at microwave frequencies. The slab
is placed between two mirrors to select Bloch standing waves and a
subwavelength spherical scatterer is scanned inside the resulting resonator.
The resonant Bloch frequencies shift depending on the electric field at the
position of the scatterer. To map the electric field component Ez we measure
the frequency shift in the reflection and transmission spectrum of the slab
versus the scatterer position. Very good agreement is found between
measurements and calculations without any adjustable parameters.Comment: 12 pages, 7 figure
Human capital accumulation and the macroeconomy in an ageing society
How do population ageing shocks affect the long-run macroeconomic performance of an economy? To answer this question we build a general equilibrium overlapping generations model of a closed economy featuring endogenous factor prices. Finitely-lived individuals are endowed with perfect foresight and make optimal choices over the life cycle. In addition to selecting age profiles for consumption and the hours of time supplied to the labour market, they also choose their schooling level and retirement age. Human capital is accumulated as a result of work experience, the extent of which is determined by the intensity of labour supply. As the agent gets older, biological deterioration sets in and human capital depreciates at an increasing rate. This ultimately prompts the agent to withdraw from the labour market. The microeconomic and macroeconomic effects of three ageing shocks are studied, namely a biological longevity boost, a comprehensive longevity boost, and a baby bust. Robustness checks are performed by allowing for capital market imperfections and indivisibility of labour supply
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